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%I #6 May 20 2019 02:45:21
%S 1,1,1,2,4,8,16,34,76,168,368,838,1964,4544,10464,24658,58984,140072,
%T 331456,795834,1932228,4665304,11227280,27305882,66953236,163418448,
%U 397826496,976658846,2412163316,5935476672,14576596320,36023097266,89458468968
%N G.f.: x * Product_{k>=1} 1/(1 - a(k)*(-x)^k)^((-1)^k).
%F Recurrence: a(n+1) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k+d)*d*a(d)^(k/d) ) * a(n-k+1).
%t a[n_] := a[n] = SeriesCoefficient[x Product[1/(1 - a[k] (-x)^k)^((-1)^k), {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 33}]
%t a[n_] := a[n] = Sum[Sum[(-1)^(k + d) d a[d]^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]/(n - 1); a[1] = 1; Table[a[n], {n, 1, 33}]
%Y Cf. A032305, A045648, A049075, A093637, A308246.
%K nonn
%O 1,4
%A _Ilya Gutkovskiy_, May 16 2019